Exponential Functions Test Answer Key with Scoring – Algebra 1

Question 1 Classify and Write the Rule (2 points)

1. Ratios 18 ÷ 6 = 54 ÷ 18 = 162 ÷ 54 = 3. Exponential: y = 6(3)^x.
2. Differences are all 7, and the value at x = 0 is 14. Linear: y = 14 + 7x.

Scoring: 1 point per part: correct type and equation together.

Question 2 Growth or Decay? (2 points)

1. 0.93 < 1, so decay. 1 − 0.93 = 0.07: decay of 7%.
2. 1.25 > 1, so growth. 1.25 − 1 = 0.25: growth of 25%.

Scoring: 1 point per part (type and rate).

Question 3 Evaluate a Decay Function (2 points)

1. f(0) = 64. f(2) = 64(0.5625) = 36. 64 and 36.
2. f(3) = 64(0.421875) = 27. 27.

Scoring: 1 point for each part.

Question 4 Equation from a Graph (3 points)

1. The y-intercept is 3, so a = 3. Ratio: 15 ÷ 3 = 75 ÷ 15 = 5, so b = 5. a = 3, b = 5.
2. y = 3(5)^x.
3. 3(5)³ = 3(125) = 375.

Scoring: 1 point per part.

Question 5 Compound Interest (2 points)

A = 3500(1.05)⁴ = 3500(1.21550625) = 4254.27…

$4,254.27

Scoring: 1 point for the correct model, 1 point for the correct value.

Question 6 A Tablet Loses Value (2 points)

1. Factor 1 − 0.15 = 0.85: V = 720(0.85)^t.
2. 720(0.7225) = 520.20: $520.20.

Scoring: 1 point per part.

Question 7 Two Plans Compared (3 points)

1. A(4) = 30 + 48 = 78. B(4) = 3(16) = 48. Plan A costs more.
2. A(5) = 90 and B(5) = 3(32) = 96, so Plan B is higher. At week 4 it was not (48 < 78). Week 5.

Scoring: (a) 1 point. (b) 1 point for computing both values at week 5, 1 point for the conclusion.

Question 8 Interpret a Mold Model (2 points)

1. 4 cm² is the starting area; 1.3 means the area grows by 30% each day.
2. 4(1.3)³ = 4(2.197) = 8.788, about 8.8 cm².

Scoring: 1 point per part.

Question 9 Line Against Curve (2 points)

x = 9: f = 900, g = 512 (line higher). x = 10: f = 1,000, g = 1,024 (curve higher).

At x = 10, g(10) = 1,024 > 1,000 = f(10), so Mia is wrong.

Scoring: 1 point for correct values at a valid x, 1 point for the conclusion.